A370159 Coefficient of x^n in the expansion of ( (1+x) * (1+x+x^2)^2 )^n.
1, 3, 19, 132, 963, 7228, 55264, 428067, 3347843, 26378079, 209065644, 1664967747, 13312423056, 106798422942, 859244421187, 6930167382832, 56015610380931, 453628706358333, 3679805451367471, 29895358350622638, 243204082036270588, 1980931117038586824
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..1000
Programs
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Mathematica
a[n_]:=SeriesCoefficient[((1+x)*(1+x+x^2)^2)^n,{x,0,n}]; Array[a,22,0] (* Stefano Spezia, Apr 30 2024 *) -
PARI
a(n, s=2, t=2, u=1) = sum(k=0, n\s, binomial(t*n, k)*binomial((t+u)*n-k, n-s*k));
Formula
a(n) = Sum_{k=0..floor(n/2)} binomial(2*n,k) * binomial(3*n-k,n-2*k).
The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x / ((1+x) * (1+x+x^2)^2) ). See A369477.